His thesis is that two distinct traits are coextensive if and only if whatever has one has both. For polar bears, the traits `being white' and `matching the environment' are clearly different traits; grasshoppers have the second but not the first. Since all polar bears have both, a theory of `selection for` has to decide which of these traits were selected for in polar bears; which, he says the Darwinian account of adaptation can't do. So there must be something wrong with the Darwinian account of adaptation. Except for being succinct, this is just a standard case of free-riding: either being white free-rides on matching the environment or matching the environment free-rides on being white. Which does the adaptationist prefer; and what is his argument for preferring it?

<a href="http://wfsc.tamu.edu/faculty/tdewitt/WFSC622/Arnold%20chapter.pdf">Lande and Arnold </a> would certainly argue that that is possible, and indeed, one of the uses that they support for G-matrix multiple regression analysis is to find out on what traits selection was "directly" working versus what traits are changing because of correlational effects.

But this use, demands that one know that G is stable through the changes in the population. And that is not only not known, but known to be unlikely in natural populations.

Of course, if one has additional information about the population -- especially the kinds of 'hands on' information that provides useful clues to the biological pathways involved -- then these kinds of G-based analyses can provide some additional insights. And that, is how I think that e.g., Steve Arnold really uses G-matrices when he uses them to study natural populations. Much of that field-based understanding of the systems in questions gets hidden in the written work, but it is what makes him confident that his results make sense.